Nat-Gr/PY0101EN-5.2_notebook_quizz_numpy2d.ipynb

## PY0101EN-5.2_notebook_quizz_numpy2d.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Get to Know a numpy Array </h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You will use the numpy array <code> A</code> for the following "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "A=np.array([[11,12],[21,22],[31,32]])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1) type using the function type "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2) the shape of the array "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 2)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3) the type of data in the array "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int64')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4) Find the second row of the numpy array <code>A</code>:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([31, 32])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[2,]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Two kinds of Multiplying  </h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "you will use the following numpy arrays for the next questions "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "A=np.array([[11,12],[21,22]])\n",
    "B=np.array([[1, 0],[0,1]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1) multiply array <code> A </code> and <code>B</code>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[11,  0],\n",
       "       [ 0, 22]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A*B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2)  plot the function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fe1f6e2a0f0>,\n",
       " <matplotlib.lines.Line2D at 0x7fe1f6e2a2e8>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "c=np.dot(A,B)\n",
    "d=np.dot(B,A)\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.plot(c,d)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "<small>Copyright &copy; 2018 IBM Cognitive Class. This notebook and its source code are released under the terms of the [MIT License](https://cognitiveclass.ai/mit-license/).</small>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python",
   "language": "python",
   "name": "conda-env-python-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
	{
	"cells": [
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"<h3> Get to Know a numpy Array </h3>"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"You will use the numpy array <code> A</code> for the following "
	]
	},
	{
	"cell_type": "code",
	"execution_count": 2,
	"metadata": {},
	"outputs": [],
	"source": [
	"import numpy as np\n",
	"A=np.array([[11,12],[21,22],[31,32]])\n"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"1) type using the function type "
	]
	},
	{
	"cell_type": "code",
	"execution_count": 3,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"numpy.ndarray"
	]
	},
	"execution_count": 3,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"type(A)"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"2) the shape of the array "
	]
	},
	{
	"cell_type": "code",
	"execution_count": 4,
	"metadata": {
	"collapsed": false,
	"jupyter": {
	"outputs_hidden": false
	}
	},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"(3, 2)"
	]
	},
	"execution_count": 4,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"A.shape"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"3) the type of data in the array "
	]
	},
	{
	"cell_type": "code",
	"execution_count": 6,
	"metadata": {
	"collapsed": false,
	"jupyter": {
	"outputs_hidden": false
	}
	},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"dtype('int64')"
	]
	},
	"execution_count": 6,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"A.dtype"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"4) Find the second row of the numpy array <code>A</code>:"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 7,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"array([31, 32])"
	]
	},
	"execution_count": 7,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"A[2,]"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"<h3> Two kinds of Multiplying </h3>"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"you will use the following numpy arrays for the next questions "
	]
	},
	{
	"cell_type": "code",
	"execution_count": 8,
	"metadata": {},
	"outputs": [],
	"source": [
	"A=np.array([[11,12],[21,22]])\n",
	"B=np.array([[1, 0],[0,1]])"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"1) multiply array <code> A </code> and <code>B</code>"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": []
	},
	{
	"cell_type": "code",
	"execution_count": 9,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"array([[11, 0],\n",
	" [ 0, 22]])"
	]
	},
	"execution_count": 9,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"A*B"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"2) plot the function"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 10,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"[<matplotlib.lines.Line2D at 0x7fe1f6e2a0f0>,\n",
	" <matplotlib.lines.Line2D at 0x7fe1f6e2a2e8>]"
	]
	},
	"execution_count": 10,
	"metadata": {},
	"output_type": "execute_result"
	},
	{
	"data": {
	"image/png": "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\n",
	"text/plain": [
	"<Figure size 432x288 with 1 Axes>"
	]
	},
	"metadata": {
	"needs_background": "light"
	},
	"output_type": "display_data"
	}
	],
	"source": [
	"c=np.dot(A,B)\n",
	"d=np.dot(B,A)\n",
	"import matplotlib.pyplot as plt\n",
	"%matplotlib inline\n",
	"plt.plot(c,d)\n"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"<hr>\n",
	"<small>Copyright © 2018 IBM Cognitive Class. This notebook and its source code are released under the terms of the [MIT License](https://cognitiveclass.ai/mit-license/).</small>"
	]
	}
	],
	"metadata": {
	"kernelspec": {
	"display_name": "Python",
	"language": "python",
	"name": "conda-env-python-py"
	},
	"language_info": {
	"codemirror_mode": {
	"name": "ipython",
	"version": 3
	},
	"file_extension": ".py",
	"mimetype": "text/x-python",
	"name": "python",
	"nbconvert_exporter": "python",
	"pygments_lexer": "ipython3",
	"version": "3.6.10"
	}
	},
	"nbformat": 4,
	"nbformat_minor": 4
	}